# GATE2004-66

8.4k views

Let $A = 1111 1010$ and $B = 0000 1010$ be two $8-bit$ $2’s$ complement numbers. Their product in $2’s$ complement is

1. $1100 0100$
2. $1001 1100$
3. $1010 0101$
4. $1101 0101$

edited

$A = 1111\quad 1010 = -6$
$B = 0000\quad 1010 = 10$
$A\times B = -60 =1100\quad 0100$

Correct Answer: $A$

edited
0
how 11111010 is -6
2

In A we can reject 1111 because single sign bit is sufficient.

And we know 2's complement is weighted code.

So 1010 = -23 *1 + 22 *0 + 21*1 + 20 * 0 = -6.

Here MSB is sign bit and 1 represents -ve.

1
Can you please tell how -60 =1100 0100
3

60 is represented as 111100. Make it 8 bits by adding 2 leading zeroes 00111100. As negative numbers are represented in 2’s complement, therefore Its 2's complement will be 1100 0100.

Explanation: Here, we have

A = 1111 1010 =  – 610 (A is a 2’s complement number)

B = 0000 1010 =  1010 (B is a 2’s complement number)

A x B = – 6010 = 1 011 11002 = 1 100 0011 (1’s complement) = 1 100 0100 (2’s complement)

Thus, the product of A and B in 2’s complement is 1100 0100, which is option A.

So, A is the correct option

0
for this question wht I did first,simply multiply both numbers and the result which I got  000100111000100

after taking 2's complement of this -2500    came.plz someone verify this.

I long it is taking long time but I want to know my mistake [email protected] @debashish

In 2's complement form

A = 11111010 = -128+64+32+16+8+2 = -6

B = 00001010 = 10

Now A* B = -60

-60 = -128+64+4 =11000100

Option : A

0
This seems somewhat understood able.
0
Does that 1 at the MSB means a negative sign?

### Convert into decimal then A= -6

There are sequence of 1's in left side delete all consecutive 1's except last one i.e;(delete four 1's from starting) This is shortcut of finding a decimal number from 2's compliment form

## How to represent (-60) in 2's compliment form?

First write +60 in binary (using 8 bit because here all options are in 8 bits)

+60 in binary=00111100

# Hence option A is right.

edited

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